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International Series in Operations Research & Management Science #11: Sample-Path Analysis of Queueing Systems

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Synopses & Reviews

Publisher Comments:

Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context.
The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.

Synopsis:

Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context. The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.

Table of Contents

Preface. 1. Introduction and Overview. 2. Background and Fundamental Results. 3. Processes with General State Space. 4. Processes with Countable State Space. 5. Sample-Path Stability. 6. Little's Formula and Extensions. 7. Insensitivity of Queueing Networks. 8. Sample-Path Approach to Palm Calculus. Appendices. A. Ergodic Theory and Random Marked Point Processes. B. Limit Theorems for Markov and Regenerative Processes. C. Stability in Stochastic Models. References. Index.

Product Details

ISBN:
9781461376200
Author:
El-taha, Muhammad
Publisher:
Springer
Author:
El-Taha, Muhammad
Author:
Stidham Jr, Shaler
Author:
Stidham, Shaler
Location:
Boston, MA
Subject:
Operations Research
Subject:
Operation Research/Decision Theory
Subject:
Probability Theory and Stochastic Processes
Subject:
OPTIMIZATION
Subject:
Business Writing
Subject:
Economics
Subject:
Language, literature and biography
Subject:
Operations Research/Decision Theory
Subject:
Business and Economics
Subject:
Distribution (Probability theory)
Subject:
Mathematical optimization
Copyright:
Edition Description:
Softcover reprint of the original 1st ed. 1999
Series:
International Series in Operations Research & Management Science
Series Volume:
11
Publication Date:
20121231
Binding:
TRADE PAPER
Language:
English
Pages:
308
Dimensions:
235 x 155 mm

Related Subjects

Business » Business Plans
Business » General
Business » Management
Business » Writing
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

International Series in Operations Research & Management Science #11: Sample-Path Analysis of Queueing Systems New Trade Paper
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$281.25 In Stock
Product details 308 pages Springer - English 9781461376200 Reviews:
"Synopsis" by , Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context. The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.
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